“I’d Do Anything For Love (But I Won’t Do That)” by Jim Steinman (with some guy named Meat Loaf on main vocals) is a pretty solid example.
You are absolutely correct. I didn’t read the OP close enough. 
I Will Always Love You - Dolly Parton
The Flying Burrito Brother’s version of “Do Right Woman”.
For once, this isn’t Rickrolling. Rick Astley, Never Gonna Give You Up.
Obvious one:
And this is also fairly obvious, but the rest of the lyrics do describe a man promising to be a good partner in a pretty healthy, realistically loving relationship:
This made me laugh, but you’re right! I’m surprised by how well the 500 miles song fits this theme, too, once I looked up the lyrics.
Specifically a good lover: Tenacious D, Fuck Her Gently
And also a great song…
Townes Van Zandt “If I Needed You”
It’s Randy Newman, so it might be a little suspect.
Randy Newman is a God among men. When Harry Nillson does an entire album of covers of your music…you’re doing something right.
Johnny Cash, I walk the line.